LOANS RECEIVABLE, NET (Details) - Schedule of the Loan Portfolio by Analyzing the Age - USD ($) $ in Thousands	Sep. 30, 2023	Sep. 30, 2022
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Current	$ 692,291	$ 625,208
Past Due	5,915	3,696
Total Past Due	5,915	3,696
Non- Accrual	5,084	2,835
Total Loans	698,206	628,904
30-59 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	147	300
Total Past Due	147	300
60-89 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	684	561
Total Past Due	684	561
90 Days + Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	5,084	2,835
Total Past Due	5,084	2,835
One-to four-family residential [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Current	236,729	213,903
Past Due	954	474
Total Past Due	954	474
Non- Accrual	386
Total Loans	237,683	214,377
One-to four-family residential [Member] \| 30-59 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due		300
Total Past Due		300
One-to four-family residential [Member] \| 60-89 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	568	174
Total Past Due	568	174
One-to four-family residential [Member] \| 90 Days + Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	386
Total Past Due	386
Commercial real estate [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Current	386,794	342,404
Past Due	2,340	387
Total Past Due	2,340	387
Non- Accrual	2,224
Total Loans	389,134	342,791
Commercial real estate [Member] \| 30-59 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Commercial real estate [Member] \| 60-89 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	116	387
Total Past Due	116	387
Commercial real estate [Member] \| 90 Days + Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	2,224
Total Past Due	2,224
Construction [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Current	19,379	12,395
Past Due	2,474	2,835
Total Past Due	2,474	2,835
Non- Accrual	2,474	2,835
Total Loans	21,853	15,230
Construction [Member] \| 30-59 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Construction [Member] \| 60-89 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Construction [Member] \| 90 Days + Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	2,474	2,835
Total Past Due	2,474	2,835
Home equity lines of credit [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Current	16,983	18,704
Past Due
Total Past Due
Non- Accrual
Total Loans	16,983	18,704
Home equity lines of credit [Member] \| 30-59 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Home equity lines of credit [Member] \| 60-89 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Home equity lines of credit [Member] \| 90 Days + Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Commercial business [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Current	30,047	34,672
Past Due	147
Total Past Due	147
Non- Accrual
Total Loans	30,194	34,672
Commercial business [Member] \| 30-59 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due	147
Total Past Due	147
Commercial business [Member] \| 60-89 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Commercial business [Member] \| 90 Days + Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Other [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Current	2,359	3,130
Past Due
Total Past Due
Non- Accrual
Total Loans	2,359	3,130
Other [Member] \| 30-59 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Other [Member] \| 60-89 Days Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due
Other [Member] \| 90 Days + Past Due [Member]
Schedule of the Loan Portfolio by Analyzing the Age [Line Items]
Past Due
Total Past Due

Loans receivable, current.

No definition available.

Name:	mgyr_LoansReceivableCurrent
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Loans receivable, past due.

+ References

No definition available.

+ Details

Name:	mgyr_LoansReceivablePastDue
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amortized cost of financing receivable on nonaccrual status. Excludes net investment in lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 16
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479319/326-20-50-16

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1405
-Paragraph (a)
-Subparagraph (3)
-Publisher SEC

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1405
-Paragraph (a)
-Subparagraph (2)
-Publisher SEC

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 7
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481962/310-10-50-7

+ Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentNonaccrualStatus
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 14
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479319/326-20-50-14

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 80
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479294/326-20-55-80

+ Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481990/310-10-45-2

+ Details

Name:	us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FinancingReceivablesPeriodPastDueAxis=us-gaap_FinancingReceivables30To59DaysPastDueMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablesPeriodPastDueAxis=us-gaap_FinancingReceivables60To89DaysPastDueMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablesPeriodPastDueAxis=us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_Residential1To4FamilyRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_ConstructionLoansMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_HomeEquityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_FinancingReceivableOtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: